Choosing wireless channel

I'm examining to what extent Omega2 can be used as a wifi range extender. Now there seems to be some confusion about what a range extender is. Some "range extenders" use the same channel as the router and re-transmits on a different SSID. In my view, a range extender is rather a device which receives packets from the wireless router and re-transmits them using the same SSID, preferably on a different radio channel.

I have three questions. I'm interested in the answers to all independently:

Can Omega2 receive on one wireless channel and transmit on another? More specifically, can the two virtual wifi interfaces (AP + STA) operate on different channels?

I tried to set my "option channel" to a specific channel rather than 'auto'. This didn't change anything. Is it not possible to choose on which channel the Omega2 AP is operating?

If operating on the same channel, is it possible to configure both AP and client to use the same SSID? Some "range extenders" seem to cope with this.